Difference between revisions of "2014 AMC 10B Problems/Problem 5"
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| − | We note that the total length must be the same as the total height because the window a square. Calling the width of each small rectangle <math>2x</math>, and the height <math>5x</math>, we can see that the length is composed of 4 widths and 5 bars of length 2. This is equal to two heights of the small rectangles as well as 3 bars of 2. Thus, <math>4(2x) + 5(2) = 2(5x) + 3(2)</math>. We quickly find that <math>x = 2</math>. The total side length is <math>4(4) + 5(2) = 2(10) + 3(2) = 26</math>, or <math>\boxed{(A)}</math>. | + | We note that the total length must be the same as the total height because the window a square. Calling the width of each small rectangle <math>2x</math>, and the height <math>5x</math>, we can see that the length is composed of 4 widths and 5 bars of length 2. This is equal to two heights of the small rectangles as well as 3 bars of 2. Thus, <math>4(2x) + 5(2) = 2(5x) + 3(2)</math>. We quickly find that <math>x = 2</math>. The total side length is <math>4(4) + 5(2) = 2(10) + 3(2) = 26</math>, or <math>\boxed{\textbf{(A)}}</math>. |
==See Also== | ==See Also== | ||
{{AMC10 box|year=2014|ab=B|num-b=4|num-a=6}} | {{AMC10 box|year=2014|ab=B|num-b=4|num-a=6}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 18:18, 20 February 2014
Problem
Doug constructs a square window using 8 equal-size panes of glass, as shown. The ratio of the height to width of each pane is 5 : 2, and the borders around and between the panes are 2 inches wide. In inches, what is the side length of the square window?
Solution
We note that the total length must be the same as the total height because the window a square. Calling the width of each small rectangle 
, and the height 
, we can see that the length is composed of 4 widths and 5 bars of length 2. This is equal to two heights of the small rectangles as well as 3 bars of 2. Thus, 
. We quickly find that 
. The total side length is 
, or 
.
See Also
| 2014 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
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